<p>An approach is presented to giving a robot the ability to move safely through a scene using its own vision that depends, as in humans, on the ability to operate explicitly in both space and time and to exploit the massive redundancy present in the hundreds of views that can be obtained when moving through a scene. The mechanism for integrating these space-time factors is a 3-D surface-building process called the Weaving Wall. In robotic navigation work the 3-D surfaces built by its process represent the space-time evolution of scene images, and this representation, in conjunction with geometric constraints, enables the 3-D structure of the scene to be determined. In other domains where there is a gradual evolution of data over a third dimension (e.g. medical tomography), the surfaces constructed by the Weaving Wall are immediately of value for their topographic structure. The designs of both the surface-building and scene-reconstruction processes make them well suited for real-time operation, given appropriate hardware.</p>